Accelerating BAO Scale Fitting Using Taylor Series

TL;DR

This paper introduces a Taylor series-based method to rapidly fit the BAO scale in galaxy surveys, significantly reducing computation time and enabling efficient analysis of large datasets for dark energy research.

Contribution

The authors develop an analytical Taylor expansion approach to estimate the BAO scale, achieving over 48-fold speedup compared to traditional numerical methods.

Findings

Method is 48-85 times faster than numerical minimization.

Achieves approximately 12,000 times speedup over standard iterative methods.

Facilitates efficient analysis for upcoming large-scale surveys like DESI.

Abstract

The Universe is currently undergoing accelerated expansion driven by dark energy. Dark energy's essential nature remains mysterious: one means of revealing it is by measuring the Universe's size at different redshifts. This may be done using the Baryon Acoustic Oscillation (BAO) feature, a standard ruler in the galaxy 2-Point Correlation Function (2PCF). In order to measure the distance scale, one dilates and contracts a template for the 2PCF in a fiducial cosmology, using a scaling factor $\alpha$. The standard method for finding the best-fit $\alpha$ is to compute the likelihood over a grid of roughly 100 values of it. This approach is slow; in this work, we propose a significantly faster way. Our method writes the 2PCF as a polynomial in $\alpha$ by Taylor-expanding it about $\alpha = 1$, exploiting that we know the fiducial cosmology sufficiently well that $\alpha$ is within a few percent of unity. The likelihood resulting from this expansion may then be analytically solved for the best-fit $\alpha$. Our method is 48-85$\times$ faster than a directly comparable approach in which we numerically minimize $\alpha$, and $\sim$$12,000 \times$ faster than the standard iterative method. Our work will be highly enabling for upcoming large-scale structure redshift surveys such as that by Dark Energy Spectroscopic Instrument (DESI).